Well, in the name of bad science, I simply logged the current 2 dwarves in my fort as the armory was being stocked. I tried to split the work evenly between the two weaponsmiths I had.
Key: Weapon Forged (Masterwork-Exceptional-Superior-Fine-Well-Ordinary) (Star = * + - )
Legendary +5 Weaponsmith (29,900 exp) 61 year old dwarf: Stress: -63 [Likes Battle Axes]
After crafting 50 (32,900 exp) Stress: -527
After crafting 100 (35,900 exp) Stress: -771
Overall unfocused by unmet needs
20 Short swords (5-13-2-0-0-0)
60 Battle axes (20-37-1-1-1-0)
20 Spears (4-11-4-0-1-0)
29% Masterworks
61% Exceptional
7% Superior
1% Fine
2% Well Crafted
Legendary +5 Weaponsmith (58,400 exp) 87 year old dwarf, Stress: 4,200
After crafting 50 (61,400 exp) Stress: 2,800
After crafting 100 (64,400 exp) Stress: 388
Overall unfocused by unmet needs
50 Short swords (8-40-1-1-0-0)
0 Battle axes (0-0-0-0-0-0)
50 Spears (14-36-0-0-0-0)
22% Masterworks
76% Exceptional
1% Superior
1% Fine
There were too many variables left uncontrolled for to draw any meaningful conclusions from this data. However I am now left with a hypothesis to test: Perhaps crafting masterworks is one way to reduce stress. If so, it is fairly easy to do if you have a modest pigtail farm. However, it could have to do with the value they created. It worked 100% of the time in these 2 cases, but could use some further testing on more advanced cases of stress, and a much larger sample size. These 2 dwarves were using steel, and so each piece is much much more valuable (and rare) than cloth. So in that case you would have to choose which dwarves to prioritize de-stressing unless you have a lot of gold or other valuable metal to pour into making hundreds upon hundreds of items. But I don't want to read too far into it.
Some item values for comparison:
Masterwork steel battle axe: 12,240 Urists
Exceptional steel battle axe: 5,100 Urists
Masterwork steel short sword: 5,040 Urists
Exceptional steel short sword: 2,100 Urists
Masterwork steel spear: 6,480 Urists
Exceptiona steel spear: 2,700 Urists
Masterwork pigtail robe: 1,052 Urists
Exceptional pigtail robe: 450 Urists
Masterwork pigtail sock: 404 Urists